Respuesta :
Answer:
base = 5 m
Step-by-step explanation:
The area (A) of a triangle is calculated using the formula
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
here h = 3b + 1 ( 1 m greater than 3 times the base ), hence
A = [tex]\frac{1}{2}[/tex] b(3b + 1) = 40
Multiply both sides by 2
b(3b + 1) = 80 ← distribute and rearrange
3b² + b - 80 = 0 ← in standard form
Consider the factors of the product of the coefficient of the b² term and the constant term which sum to give the coefficient of the b- term
product = 3 × - 80 = - 240 and sum = 1
The factors are - 15 and + 16
Use these factors to split the b- term
3b² - 15b + 16b - 80 = 0 ( factor the first/second and third/fourth terms )
3b(b - 5) + 16(b - 5) = 0 ← factor out (b - 5)
(b - 5)(3b + 16) = 0
Equate each factor to zero and solve for b
b - 5 = 0 ⇒ b = 5
3b + 16 = 0 ⇒ b = - [tex]\frac{16}{3}[/tex]
However, b > 0 ⇒ b = 5
The base of the triangle is 5 m
